What is 4^{t-6}u(t-6)e^{-4t}cosh(9t) ?

The solution to 4^{t-6}u(t-6)e^{-4t}cosh(9t) is (4^{t-6}ucosh(9t)(t-6))/(e^{4t)}

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simplify 4^{t-6}u(t-6)e^{-4t}cosh(9t)

simplify

4^{t - 6} u (t - 6) e^{- 4 t} cosh (9 t)

\frac{4 ^{t - 6} u cosh ( 9 t ) ( t - 6 )}{e ^{4 t}}

Solution steps

4^{t - 6} u (t - 6) e^{- 4 t} cosh (9 t)

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= 4^{t - 6} \cdot \frac{1}{e ^{4 t}} u cosh (9 t) (t - 6)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 4 ^{t - 6} u ( t - 6 ) cosh ( 9 t )}{e ^{4 t}}

Multiply:

1 \cdot 4^{t - 6} = 4^{t - 6}

= \frac{4 ^{t - 6} u cosh ( 9 t ) ( t - 6 )}{e ^{4 t}}

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What is 4^{t-6}u(t-6)e^{-4t}cosh(9t) ?
The solution to 4^{t-6}u(t-6)e^{-4t}cosh(9t) is (4^{t-6}ucosh(9t)(t-6))/(e^{4t)}